Il faut modifier la distance

If you want to extract the buffer, first you must check the projection between imported layer and buffer. Layer and buffer must always have the equal projections. Second, if you want to extract buffer of the mile of radius, you may check it is a lot of points (data) belong in an analysis to this volume of radius if for example most of the points belong to the radius less than 100 m, the buffer cannot be created.

I agree with Aleksandar Dordje Valjarevic the prime requirement is to keep both files on same projection. Visual appearance of size of the buffer depends on scale of visualization, we can measure the diameter of the resulted buffer through scale tool and if it shows the correct value than our buffer is accurate.

Hello I think it's your point layer that poses a problem. When you create it in arccatalog you have to indicate that you want to use the same projection system as your city layer. You can then create or import your points in this layer. Then check that you have the correct unit of measure for your buffer in the function parameters.